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2x(3x-41)+(2x+7)+(2x+7)=360
We move all terms to the left:
2x(3x-41)+(2x+7)+(2x+7)-(360)=0
We multiply parentheses
6x^2-82x+(2x+7)+(2x+7)-360=0
We get rid of parentheses
6x^2-82x+2x+2x+7+7-360=0
We add all the numbers together, and all the variables
6x^2-78x-346=0
a = 6; b = -78; c = -346;
Δ = b2-4ac
Δ = -782-4·6·(-346)
Δ = 14388
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14388}=\sqrt{4*3597}=\sqrt{4}*\sqrt{3597}=2\sqrt{3597}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{3597}}{2*6}=\frac{78-2\sqrt{3597}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{3597}}{2*6}=\frac{78+2\sqrt{3597}}{12} $
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